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- Probabilistic risk analysis : foundations and methods
- Probabilistic risk analysis: foundations and methods
- Probabilistic risk analysis

Bedford , R. Probabilistic risk analysis: foundations and methods. N2 - Probabilistic risk analysis aims to quantify the risk caused by high technology installations. Increasingly, such analyses are being applied to a wider class of systems in which problems such as lack of data, complexity of the systems, uncertainty about consequences, make a classical statistical analysis difficult or impossible. The authors discuss the fundamental notion of uncertainty, its relationship with probability, and the limits to the quantification of uncertainty.

## Probabilistic risk analysis : foundations and methods

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Probabilistic risk analysis : foundations and methods Home Probabilistic risk analysis : foundations and methods. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press First published Sixth printing Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Bedford T.

Includes bibliographical references and index. ISBN 0 2 1. Reliability Engineering —Mathematics. Risk assessment. Cooke, Roger M. Scope of probabilistic risk analyses Risk analysis resources 1. The meaning of meaning The meaning of uncertainty Probability axioms 2. Utility Multi-attribute decision theory and value models It has been developed from course notes used at Delft University of Technology.

An MSc course on risk analysis is given there to mathematicians and students from various engineering faculties. The mathematical background required varies from topic to topic, but all relevant probability and statistics are contained in Chapters 3 and 4. When such an event does occur then the underlying systems and organizations are often changed so that the event cannot occur in the same way again.

Because of this, the probabilistic risk analyst must have a strong conceptual and mathematical background. Chapters 3 and 4 provide the technical background in probability and statistics that is used in the rest of the book. The remaining chapters are more-or-less technically independent of each other, except that Chapter 7 must follow Chapter 6, and 14 should follow Almost all the chapters are concluded with exercises.

Special thanks go of course to our families and friends for putting up with us during the preparation of this manuscript. In many of these areas PRA techniques have been adopted as part of the regulatory framework by relevant authorities. In other areas the analytic PRA methodology is increasingly applied to validate claims for safety or to demonstrate the need for further improvement. The trend in all areas is for PRA to support tools for management decision making, forming the new area of risk management.

Since PRA tools are becoming ever more widely applied, and are growing in sophistication, one of the aims of this book is to introduce the reader to the main tools used in PRA, and in particular to some of the more recent developments in PRA modeling. Another important aim, though, is to give the reader a good understanding of uncertainty and the extent to which it can be modeled mathematically by using probability.

We believe that it is of critical importance not just to understand the mechanics of the techniques involved in PRA, but also to understand the foundations of the subject in order to judge the limitations of the various techniques available. The most important part of the foundations is the study of uncertainty. What do we mean by uncertainty?

How might we quantify it? After the current introductory chapter, in Part two we discuss theoretical issues such as the notion of uncertainty and the basic tools of probability and statistics that are widely used in PRA.

Part three presents basic modeling tools for engineering systems, and discusses some of the techniques available to quantify uncertainties both on the basis of reliability data, and using expert judgement. In Part four we discuss uncertainty modeling and risk measurement. The aim is to show how dependent uncertainties are important 3 4 1 Probabilistic risk analysis and can be modeled, how value judgements can be combined with uncertainties to make optimal decisions under uncertainty, and how uncertainties and risks can be presented and measured.

These numerical safety goals were not adopted in the subsequent shuttle program. These numbers are then taken as fact, instead of what they really are: subjective evaluations of hazard level and probability. An extensive review of the NASA safety policy following the Challenger accident of January 28, brought many interesting facts to light. NASA management rejected this estimate and elected to rely on 1. Rather, initial estimates of catastrophic failure probabilities were so high that their publication would have threatened the political viability of the entire space program.

By contrast, a congressional report on the causes of the Shuttle accident quoted in [Garrick, ] concluded that the qualitative method of simply identifying failures leading to loss of vehicle accidents the so-called critical items was limited because not all elements posed an equal threat. Since the shuttle accident, NASA has instituted programs of quantitative risk analysis to support safety during the design and operations phases of manned space travel. With this assessment in hand, NASA was able to convince the US Congress that the money spent on shuttle development since the Challenger accident had been well used, even though no failure paths had been eliminated.

A board of inquiry [ESA, ] revealed that the disaster was caused by software errors and the management of the software design. An early study released in focused on three scenarios of radioactive releases 6 1 Probabilistic risk analysis from a megawatt nuclear power plant operating 30 miles from a large population center.

Successive design improvements were intended to reduce the probability of a catastrophic release of the reactor core inventory. Such improvements could have no visible impact on the risk as studied with the above methods. As mentioned above, the basic methods of probabilistic risk assessment originated in the aerospace program in the s. The panel was led by Prof. However, the dramatic events of March served to change that. Subsequent study of the accident revealed that the accident sequence had been predicted by the Reactor Safety Study.

The probabilities associated with that sequence, particularly those concerning human error, do not appear realistic in hindsight. They also questioned whether the NRC was capable of regulating the risks of nuclear energy, and recommended that the regulatory body be massively overhauled which recommendation was not carried out.

Shortly thereafter a new generation of PRAs appeared in which some of the methodological defects of the Reactor Safety Study were avoided. At the beginning of the test some of the main coolant pumps slowed down, causing a reduction of coolant in the core.

This caused a sudden increase in power which could not be controlled because the control systems worked too slowly.

The power surge caused the fuel to overheat and disintegrate. Thousands of people have been displaced and blame the reactor accident for all sorts of health problems.

The Three Mile Island and Chernobyl accidents, in addition to regular publicity about minor leaks of radioactive material from other power stations and processing plans, however, have fostered a climate of distrust in nuclear power and in the capacity of management to run power stations properly. Besides technical advances in the methodology of risk analyses, the s and s have seen the further development of numerical safety goals.

The impetus for much of this work was the Post-Seveso Directive [EEC, ] adopted by the European Community following the accidental release of dioxin by a chemical plant near Seveso, Italy. The directive institutes a policy of risk management for chemical industries handling hazardous 1.

The Dutch government took the lead in requiring quantitative risk analyses of potentially hazardous objects, and has invested heavily in developing tools and methods for implementing this policy. This lead has been followed by several other member countries. About 70 companies in the Netherlands fall under this reporting requirement. EVRs are to be updated every 5 years.

The quantitative risk analysis required in EVRs may be broken down into four parts. The third part calculates the probability of damage, consisting of the probability of an undesired release of hazardous substances, and the probability of propagation through the environment causing death. The fourth part determines the individual and group risk associated with the installation.

An overview of some of the risk goals currently set is given in Table The reader interested in looking further into the past is referred to [Covello and Mumpower, ] which starts about BC, and [Bernstein, ]. The limitations of the mathematical approach to measuring risk will be highlighted in Chapter Our discussion here is largely drawn from [Kaplan and Garrick, ].

Risk curve A hazard is considered as a source of danger but the concept does not contain any notion of the likelihood with which that danger will actually impact on people or on the environment.

We are often uncertain about whether or not a hazard will actually lead to negative consequences that is, whether the potentiality will be converted into actuality. A risk analysis tries to answer the questions: i What can happen? If the scenarios are ordered in terms of increasing severity of the consequences then a risk curve can be plotted, for example as shown in Figure 1.

The risk curve illustrates what is the probability of at least a certain number of casualties in a given year. First, instead of talking about the probability of an event, they talk about the frequency with which such an event might take place.

This more sophisticated notion of risk will be discussed further in Chapter 2. The tools that will be described in this book are dedicated to these tasks. The nuclear sector has made the largest commitments of resources in this area. Some of the larger chemical process studies have been of comparable magnitude, although the studies performed in connection with the Post-Seveso Directive tend to be much smaller.

In the aerospace sector, the methods have not yet been fully integrated into the existing design and operations management structures, although the United Space Alliance the consortium operating the space shuttle for NASA is probably currently the furthest in an integrated risk management approach.

The Procedures Guide [NRC, ], gives a detailed description of the various levels of commitment of resources in nuclear PRAs, and we summarize this below, as the general format is applicable to other sectors as well.

Three levels are distinguished: level 1, systems analysis; level 2, systems plus containment analysis; level 3, systems, containment and consequence analysis. These are explained further below. In the case of a nuclear reactor, this concerns primarily the release of radioactive material from the reactor core.

In addition the economic impact of land interdiction, clean-up, relocation etc. Papers on risk analysis are to be found in engineering journals and also in a number of interdisciplinary journals.

The Society for Risk Analysis and 1. Part II Theoretical issues and background 2 What is uncertainty? Unfortunately, in order to be practical, one must occasionally dabble in philosophy. An opening chapter on uncertainty is one of those occasions. Formulating a clear, consistent and workable point of view at the beginning prevents confusion and ambiguity from cumulating and erupting at inopportune moments. Having done that, we can be uncertain about whether the precipitation count in what we agree to call Cincinnati on Jan.

Less straightforward is II The number of atoms in the universe is In this sense we can be uncertain about II. More precisely, we are uncertain about how exactly II would be resolved, and uncertain about what the resolution would be; but we are certain that it can in principle be resolved.

## Probabilistic risk analysis: foundations and methods

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Bedford and R. Bedford , R. Probabilistic risk analysis aims to quantify the risk caused by high technology installations. Increasingly, such analyses are being applied to a wider class of systems in which problems such as lack of data, complexity of the systems, uncertainty about consequences, make a classical statistical analysis difficult or impossible.

PDF | On Jan 1, , Tim Bedford and others published ccofmc.org probabilistic-risk-analysis-foundations-and-method | Find, read and cite all.

## Probabilistic risk analysis

Uncertainty and Risk pp Cite as. The methods of engineering probabilistic risk analysis and expected-utility decision analysis share a common core: a probabilistic model of occurrences of uncertain events. This model is based on systems analysis and on the identification of an exhaustive and mutually exclusive set of scenarios, their probabilities and their consequences. The major differences are rooted in the nature and the framing of the problems that they address.

Collapse risk analysis is of great significance for ensuring construction safety in foundation pits. This study proposes a comprehensive methodology for dynamic risk analysis of foundation pit collapse during construction based on a fuzzy Bayesian network FBN and a fuzzy analytical hierarchy process FAHP. Firstly, the potential risk factors contributing to foundation pit collapse are identified based on the results of statistical analysis of foundation pit collapse cases, expert inquiry, and fault tree analysis. Then, a FAHP and improved expert elicitation considering a confidence index are adopted to elicit the probability parameters of the BN.

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*Zan, Kun, and J. Eric Bickel.*

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